Distinguishing between classes of time series sampled from dynamic systems is
a common challenge in systems and control engineering, for example in the
context of health monitoring, fault detection, and quality control. The
challenge is increased when no underlying model of a system is known,
measurement noise is present, and long signals need to be interpreted...
paper we address these issues with a new non parametric classifier based on
topological signatures. Our model learns classes as weighted kernel density
estimates (KDEs) over persistent homology diagrams and predicts new trajectory
labels using Sinkhorn divergences on the space of diagram KDEs to quantify
proximity. We show that this approach accurately discriminates between states
of chaotic systems that are close in parameter space, and its performance is
robust to noise.